How this instrument works
Coherence length is the distance a light wave can travel before its phase drifts far enough from a delayed copy of itself that the two can no longer interfere predictably. A mathematically perfect single-frequency wave would stay in step with itself forever, but no real laser emits at one exact wavelength — it emits across a narrow band of width Δλ centered on λ, the spectral linewidth, and that spread is what caps the distance.
The λ² ⁄ Δλ shape comes from converting the linewidth between wavelength and frequency. Since c = λν, a small spread in wavelength maps to a frequency spread of Δν ≈ cΔλ ⁄ λ², and the coherence time is roughly the inverse of that spread, τc ≈ 1 ⁄ Δν. Multiplying by the speed of light to turn a time into a distance, L_c = c·τc, cancels one factor of λ and leaves a second one on top — so wavelength enters twice while linewidth enters once, which is why a longer-wavelength source needs a proportionally narrower absolute linewidth to match the coherence length of a shorter one.
The formula assumes a single, well-behaved emission line and a linewidth much smaller than the wavelength itself, the regime where the frequency-spread approximation holds. It says nothing about a laser running on several separated longitudinal modes, and it describes the source alone — a long fiber run, a beamsplitter, or ordinary phase noise picked up along the path can erode usable coherence well before the source's own limit is reached, so a measured interference contrast downstream is never larger than this number and is usually smaller.
- Enter the "Center wavelength" — the laser's nominal emission wavelength, for example 1550 nm for a telecom C-band diode; switch the unit menu to µm if the datasheet lists it that way.
- Enter "Spectral linewidth, nm" — the full spectral width from the same datasheet. If it is quoted in MHz or kHz instead, convert first: Δλ = λ²Δν ⁄ c.
- Read "Coherence length" for the result. Switch its unit between mm, m, and km to match the scale of the system you are checking.
- Halve or double the "Spectral linewidth, nm" value and watch "Coherence length" respond by the same factor in the opposite direction — the two are strictly inverse.
Worked example — coherence length of a 1,550 nm DFB laser
A distributed-feedback (DFB) laser in a telecom transmitter is specified with a center wavelength of 1550 nm (1.55×10⁻⁶ m) and a spectral linewidth of 0.0001 nm, which is 0.1 picometre or 1×10⁻¹³ m. Plugging both into L_c = λ² ⁄ Δλ gives (1.55×10⁻⁶)² ÷ 1×10⁻¹³ = 24.025 metres of coherence length.
Twenty-four metres feels short next to the kilometres of fibre the signal will travel, and that gap is the point: 0.1 pm corresponds to roughly a 12.5 MHz frequency linewidth, typical of an ordinary DFB diode, not the kHz-level external-cavity or fibre lasers that long-haul coherent systems and precision interferometry specify when they actually need coherence measured in kilometres rather than metres.
Questions
What exactly does coherence length measure?
The propagation distance over which a light wave keeps a predictable phase relationship with a delayed copy of itself, so the two can still produce a clear interference pattern. Beyond that distance the phase has drifted enough that fringes wash out. It describes the source's own spectral purity, not the medium the light later travels through.
Why does coherence length depend on wavelength squared, not just wavelength?
Because the formula first converts a wavelength spread into a frequency spread, Δν ≈ cΔλ ⁄ λ², which already carries a λ² in the denominator. Coherence length is c divided by that frequency spread, so the λ² flips back to the numerator — a longer-wavelength source needs a proportionally narrower linewidth just to match a shorter-wavelength source's coherence length.
My laser's datasheet lists linewidth in kHz or MHz — how do I use this calculator?
Convert the frequency linewidth to a wavelength linewidth first: Δλ = λ²Δν ⁄ c. For a 1550 nm laser with a 100 kHz linewidth, that works out to about 8×10⁻¹⁶ m, roughly 8×10⁻⁷ nm — enter that figure into "Spectral linewidth, nm" and the calculator returns the coherence length directly.
Does a longer coherence length always make a laser better?
Not automatically. Long coherence length matters for interferometry, LIDAR ranging, and dense wavelength-division multiplexing, where the signal must stay coherent with itself over the full path length. But squeezing linewidth down to get there also lowers the threshold for nonlinear effects like stimulated Brillouin scattering in high-power fibre systems, so narrower is a design tradeoff, not an unconditional win.
What is the difference between coherence length and coherence time?
Coherence time τc is how long the phase stays predictable; coherence length is how far the wave travels in that time, L_c = c·τc. They describe the same underlying property — spectral purity — measured in seconds versus metres, and either one converts to the other once the speed of light is brought in.
Why does a broader linewidth shorten the coherence length by the same factor?
Because the relationship is a simple inverse proportion once wavelength is fixed: doubling Δλ halves L_c exactly. At a fixed 1550 nm, a linewidth of 1 picometre gives 2.4025 metres of coherence length, ten times less than the 24.025 metres a linewidth of 0.1 picometre gives — the same ten-times relationship holds at any wavelength.